LAHAINA, Hawaii — As No. 9 North Carolina began to chip away at a lead that, at one time, had been as high as 29 points in the second half, UNC used scrappy defense and took advantage of Butler mistakes to claw its way back into the Maui Invitational semifinal matchup.

Unfortunately for the Tar Heels, that version of the North Carolina squad was noticeably absent for the first 32 minutes of Tuesday’s game, one that would eventually end in a 82-71 victory for the Bulldogs (3-1).

Scoring only 18 points in the first half, its lowest total since a 1996 game against Wake Forest, UNC (4-1) showed a severe lack of intensity in the opening minutes, and Butler used a 10-2 run to grab an early lead. UNC was outrebounded 24-12 in the first half and went into the break with just a single offensive board.

The second half wasn’t much better for the Tar Heels, who trailed Butler 60-31 with just less than 12 minutes to play. It would have been easy to count UNC out. Butler coach Brad Stevens knew better than that.

“(I was) just a little surprised,” Stevens said about his team’s major advantage. “We’ve been in that spot both ways before. You never give up … when you’re playing a program like Carolina, you know they’re coming. Their run’s coming next.”

A Reggie Bullock 3-pointer, just his second basket of the night, brought the Tar Heels back from the depth of their 29-point despair, and 30 seconds later, P.J. Hairston drained another deep bucket to kick off an 11-0 run.

UNC would gradually eat away at Butler’s lead for the rest of the game. Every time the Tar Heels made a significant gain, though, the Bulldogs would respond with a 3-pointer to all but negate their progress.

Butler, which shot 47 percent from the floor, made 12 3-pointers Tuesday and went 7-for-9 in the second half. Bullock and Hairston admitted the Bulldogs’ screens stumped them, leading to their opponent’s offensive efficiency.

“I felt like that was the difference between the two teams today,” said Hairston, who led UNC with 15 points. “They set way better screens on their offensive end, but on our offensive end we were setting screens but Butler was fighting right through them, showing they were more aggressive.”

With 1:40 left to go, UNC trailing by 12, freshman point guard Marcus Paige scored six straight points to bring the Tar Heels the closest they would ever come in the second half.

The Tar Heels then hurled a series of quick, desperation 3-pointers — the very things that Butler successfully used to all but drive the nail in North Carolina’s coffin moments earlier — to try to close the deal. Each one fell just a little bit short.

Williams isn’t exactly sure which team, the one that began the game or the one that came close to coming back in the end, is the true character of North Carolina.

“We’re probably not nearly as exciting as we were (against Mississippi State), and I hope to dickens we’re not as bad as we were when we were down 29 tonight,” Williams said.

But of one thing, he’s sure.

“We’ve got to learn from this,” he said. “On game nights, you’ve got to frickin’ step up and be a man.”